Couple Stress Theory Research Articles

Poroelastic size dependent dynamics of viscoelastic microbeams connected via a viscoelastic layer

This article aims to investigate the dynamics of clamped-clamped porous viscoelastic double microbeams interconnected via a viscoelastic layer within the framework of the modified couple stress theory (MCST). Different types of porosity distributions are considered to examine the material imperfection effects on the dynamics of the double microbeam. A closed-cell porosity model is employed to model the variation of the material properties in the thickness plane. The coupled longitudinal and lateral equations of motion are derived using Hamilton’s principle. The governing equations of motion are solved using the modal decomposition method. The equations of motion are verified against the literature for simplified cases (i.e., a non-porous single viscoelastic microbeam and a porous single microbeam resting on a viscoelastic foundation). The numerical results are validated for simpler versions of the system using the finite element method and against the existing literature for a simplified case of a uniformly distributed porous double macrobeam connected via an elastic layer. Influences of viscoelasticity in the double microbeam, viscoelastic layer, porosity, and small-scale influences on the dynamics of the viscoelastic double microbeams are studied. It was found that increasing the material length-scale factor causes the complex fundamental lateral vibrational frequencies to increase for all the porosity patterns.

Nonlinear deterministic dynamic analysis of a GPL micropipe conveying pulsating laminar flow

In several industries, the handling of fluid-filled micropipes is common. New-brand structures are increasingly being manufactured using advanced materials. This article tackles one of the crucial dynamic analyses that an advanced fluid-filled micropipe encounters. The dynamics of a graphene nanoplatelets-reinforced micropipe (GPL micropipe) under pulsating laminar flow for the first time is examined. The Euler-Bernoulli beam model follows the modified couple stress theory (MCST) and von-Karman’s nonlinear strain to formulate the problem. The impression of the flow profile exerted by a real flow as a consequence of fluid viscosity, is taken into account. The plug flow model results are compared to those regarding real flow consideration. Using the method of multiple scales (MMS), we determine the instability area and the steady state response of the GPL micropipe subjected to the principal parametric resonance of one of its modes due to pulsating laminar flow by applying this method to the discretized couple nonlinear gyroscopic governing equations. The Floquet theory treats the linear equations and fourth-order Runge–Kutta (RK4) method attacks nonlinear ones to validate MMS findings. It is confirmed that the 0.3 % addition of the GPL to matrix phase significantly enhances its advanced attributes, making it a highly effective material. The GPL reinforcement phase in the FGO pattern increases the critical flow velocity that exhibits the micropipe to static instability by 37.98 % , and critical flow stimulation amplitude fraction by 152.19 % , while declines instability area bandwidth by 36.95 % , and steady state response by 67.17 % relative to a non-reinforced micropipe. A denser flow degrades the corresponding values by 18.40 % , 42.59 % , 41.67 % , and 227.28 % in comparison to a lighter fluid. The declared findings provide crucial insights into the key design elements affecting significantly the functioning of fluid-filled GPL micropipes system, and regulate future research and expand openings for industry applications.

Pull-in instability and nonlinear vibration of microbeam with piezoelectric patch driven by electrostatic force using modified couple stress theory

The static and dynamic pull-in characteristics of electrostatically and piezo-electrically actuated microbeam are investigated. The static pull-in voltage is evaluated using analytical methods based on MCST, CCMT and validated through the use of FE based COMSOL multiphysics tools. The dynamic pull-in voltage obtained from numerical technique and verified with existing literature, lower than the static pull-in voltage. The piezoelectric patch has a significant influence on the pull-in voltage and an effect on the aspect ratio. Moreover, the pull-in band and instability zone of the microbeam with weak and hard forcing function have been investigated using multiple scale method.

Electro-magneto-mechanical critical load analysis of piezoelectric/piezomagnetic sport force plates used for testing athlete performance

Electro-magneto-thermo-mechanical critical loads of a sandwich microplate composed of a core integrated with piezoelectric/piezomagnetic face-sheets are analyzed in this paper based on higher order shear and normal deformation theory and modified couple stress theory. The constitutive relations are developed based on generalized Hooke’s law and electromagnetic relations. In order to measure athletic performance and his/her quantitatively or qualitatively grades, a force plate is used. The thickness stretching of the sport force plates is accounted based on a new function in displacement field. The electric and magnetic potentials are assumed as summation of a linear function including applied electric/magnetic potential and two functions for satisfying the zero condition at top and bottom of the sport force plates.

Vibration analysis of rectangular nanoplate immersed in viscous fluid based on modified couple stress theory

Vibration analysis of rectangular nanoplate immersed in viscous fluid based on modified couple stress theory

Stability and vibration control of electrostatically excited functionally graded microresonator using nonlinear observer based sliding mode controller

The dynamic stability analysis of microsystems is an important aspect in understanding the critical operating regions under different excitations. Present study proposes an observer-based adaptive back-stepping sliding mode controller (ABSMC) model to control and stabilize an electrostatically excited functionally graded microresonator. The dynamic model of a microsystem subjected to random disturbances is derived using modified couple stress theory and Euler–Bernoulli’s beam model. The effective material properties are obtained from Mori-Tanaka scheme and the equations of motion are derived using Hamilton principle and solved by Galerkin’s method. A trained neural network estimator predicts the disturbances and the adaptive back-stepping sliding mode controller is designed for improving the system stability. The results of the proposed controller are compared with conventional sliding mode control (SMC) and proportional-derivative (PD) control solutions and it is found that ABSMC reduces settling time and input control force by 52.42% and 88.40%, respectively, with minimal chattering. The proposed control methodology effectively extends the travelling range of FG microsystems within and beyond the pull-in voltage.

Phase field thermal shock analysis of rotating porous cracked pretwisted FGM microblade using exact shear correction factor

The present work is an attempt to develop a simple and accurate finite element formulation for the thermal shock analysis of the rotating porous cracked pretwisted functionally graded material (FGM) microblade using modified coupled stress theory in conjunction with phase-field and first-order shear deformation theory (FSDT). The physical neural surface is taken as the reference plane and the exact value of the shear correction factor is calculated from the shear stiffness. The elastic properties are assumed to be temperature-dependent and the upper ceramic layer is subjected to a high thermal shock whereas the bottom metallic layer is maintained at room temperature or is thermally insulated. The governing differential equation for the present analysis is derived using Hamilton’s principle and Newmark average acceleration method is used to obtain the transient response of the rotating porous cracked pretwisted FGM microblade subjected to thermal shock. The results obtained from the present finite element formulation are first validated with several benchmark examples available in the literature. New results are presented investigating the effect of crack depth, crack location, crack angle, rotational velocity and material scale ratio on the transient response of the cracked rotating porous pretwisted FGM microblade subjected to thermal shock. It is shown here that the parameters like crack depth, crack location and crack angle have a significant influence on the transient response of the rotating porous cracked pretwisted FGM microblade.

Static bending analysis of BDFG nanobeams by nonlocal couple stress theory and nonlocal strain gradient theory

This paper presents analytical solutions for the bending behavior of bi-directional functionally graded (BDFG) micro and nanobeams, wherein the material properties vary along both the thickness and axial directions, following power-law and exponential-law profiles, respectively. This study employs two size-dependent theories, nonlocal modified couple stress theory (NCST) and nonlocal strain gradient theory (NSGT), to account for size effects inherent in nanoscale structures. The governing differential equations are derived using Hamilton's principle, and the Laplace transform technique is utilized for their solution. The study critically compares the size effects captured by NCST and NSGT and assesses the influence of material gradation parameters in both directions. Additionally, the impacts of nonlocal and length scale parameters are thoroughly investigated. The findings indicate that NSGT tends to overestimate size effects compared to NCST. This research enhances the understanding of the mechanical behavior of BDFG nanobeams, offering valuable insights for the design and analysis of nanoscale structures across diverse applications.

Size-dependent finite element buckling analysis of porous cylindrical micro-shells reinforced by graphene platelets

This study introduces a spatial shear deformable rectangular element formulation to investigate the size-dependent buckling behavior of porous graphene platelets (GPL) reinforced micro-shells within the framework of the modified couple stress theory (MCST) for the first time in the worldwide term. The rectangular element, characterized by 4 nodes with 19 degrees of freedom each and possessing weak continuity of order C 1 , incorporates a length scale parameter enabling size-dependent analyses of shells. The research considers three distinct functions for the distribution of porosity combined with three different patterns of the GPL distribution (called by patterns A to C) along the micro-shell thickness. The elastic modulus of the nanocomposite in the absence of porosity is obtained using the Halpin-Tsai micromechanics model. Subsequently, the study meticulously validates the modeling accuracy and then investigates variations in the critical buckling load with respect to porosity distribution functions, distribution patterns of GPL, porosity coefficient, weight percentage of GPL, geometric parameters of the cylinder, and the length-scale parameter. The results reveal that the combination of the GPL pattern A with the first symmetric type porosity distribution yields the highest critical buckling loads. On the contrary, if the pattern B is combined with the second symmetric type of porosity distribution, the lowest critical buckling load will be observed. Given the accuracy of the results obtained and the versatility of the finite element method (FEM) in handling complex geometries together with diverse boundary conditions, the developed element holds promise for analyzing shells of various shapes under different boundary conditions.

Numerical verification of torsion-bar models based on the modified couple stress theory

This study verifies the suitability of the classical Saint–Venant’s displacement field, originally intended for macroscale torsional behavior, to microscale torsion-bar models within the modified couple stress theory framework. Finite element analysis was conducted for bars with circular and rectangular cross-sections, and the results align closely with analytic solutions, which is confirmed by the energy ratio analysis. These results affirm the appropriateness of the displacement field for microscale torsion bars. Additionally, warping effects are observed to be minimal, even at the microscale. These findings validate torsion experiments for determining a material’s length scale parameter, advancing the understanding of microscale torsion.

Examination of the complementary energy principle in modified couple stress theory and its application for analysis of size effects in the internal force field of functionally graded microbeams

The precise quantification of the internal force field in MEMS piezoresistive sensor micro structure is crucial for ensuring accurate signal output. This paper proposes and proves the complementary energy principle associated with modified couple stress theory (MCST) based on the linear elasticity assumption. And this principle is used to discuss and analyze whether there is a size effect in the internal force field of functionally graded (FG) micro beams for the MEMS piezoresistive sensor. The results show that the size effects exist in the internal forces and the stationary point coordinate x of the total moment for the micro beam. The size effects are related to the dimensionless material scale parameter l/h, the supported spring stiffness, the temperature and the support rotational movements. Intuitive explanations of the size effects are given for the internal force fields and its stationary point coordinates. Behaviors of the solutions agree with the published data when the MCST degenerates into the classical theory (CT).

Nonlinear dynamic analysis of an inclined micro-beam under a moving mass

Nonlinear vibration of an inclined simply supported micro-beam under a moving mass is investigated for Euler–Bernoulli beam theory (EBT) and Timoshenko beam theory (TBT) respectively. Based on a modified couple stress theory (MCST) and the von-Karman geometric nonlinearity, the nonlinear coupled dynamic equations of the system are established through the Hamilton’s principle with the assumed mode method. A wide range of numerical examples are employed to study the influence of slenderness ratio, cross-section height, inclined angle, the size and velocity of the moving mass and the scale factor of the material on the solutions of nonlinear and linear, the solutions of EBT and TBT and the solutions of moving mass and moving load. By comparing the differences between the nonlinear and linear solutions under different parameters and beam theories, the importance and significance of nonlinear dynamic analysis of the inclined micro-beam are revealed.

Size-Dependent Analysis of Strain Energy Release Rate of Buckling Delamination Based on the Modified Couple Stress Theory

Size-Dependent Analysis of Strain Energy Release Rate of Buckling Delamination Based on the Modified Couple Stress Theory

On the Applications of a New Advanced PEPFG Mathematical Model for HTM Dynamic Behavior of SDF Sandwich Plates

Considering the crucial role of the flexoelectricity phenomena (the electrical polarization–strain gradient coupling) in the mechanical behavior of different structures on the micro/nanoscale, this paper is derives the motion equations of a size-dependent flexoelectric (SDF) sandwich plate to study its hygro-thermo-mechanical (HTM) dynamic behavior. The model is a three-layer microplate including a porous exponential and power–law functionally graded (PEPFG) mid-layer, and two flexoelectric face sheets. The whole structure is under hygrothermal loading and the Vlasov foundation serves as the stand for the structure. Then, Hamilton’s principle and modified couple stress theory (MCST) are implemented to derive the motion equations. The new PEPFG utilization besides evaluating the impact of the length scale parameter, hygrothermal loading, materials composition, porosity, foundation parameter, and boundary conditions on the normalized natural frequency (NNF) of such an SDF sandwich model is the novelty of this paper. It is revealed that the lateral ratio enhancement causes NNF and stiffness reduction in the model. Furthermore, among all considered boundary types, simply supported and clamped refer to the lowest and the highest NNFs, respectively. This paper serves as a good source to provide a better understanding of the dynamic response of high stiffness-to-weight ratio structures to different variable variations.

Size-Dependent Finite Element Analysis of Functionally Graded Flexoelectric Shell Structures Based on Consistent Couple Stress Theory

The functionally graded (FG) flexoelectric material is a potential material to determine the structural morphing of aircrafts. This work proposes the penalty 20-node element based on the consistent couple stress theory for analyzing the FG flexoelectric plate and shell structures with complex geometric shapes and loading conditions. Several numerical examples are examined and prove that the new element can predict the size-dependent behaviors of FG flexoelectric plate and shell structures effectively, showing good convergence and robustness. Moreover, the numerical results reveal that FG flexoelectric material exhibits better bending performance and higher flexoelectric effect compared to homogeneous materials. Moreover, the increase in the material length scale parameter leads to a gradual increase in the natural frequencies of the out-of-plane modes of FG flexoelectric plate/shell, while the natural frequencies of the in-plane modes change minimally, resulting in the occurrence of mode-switching phenomena.

Size-dependent nonlinear free vibration of magneto-electro-elastic nanobeams by incorporating modified couple stress and nonlocal elasticity theory

Magneto-Electro-Elastic (MEE) Composites, as an innovative functional material blend, are composed of multiple materials, boasting exceptional strength, rigidity, and an extraordinary magneto-electric interaction effect. This paper establishes a nonlocal modified couple stress (NL-MCS) magneto-electro-elastic nanobeam dynamic model. To accurately capture the intricate influences of scale effects on nanostructures, This model meticulously examines scale effects from two distinct perspectives: leveraging nonlocal elasticity theory to elucidate the softening phenomena in nanostructures stemming from long-range particle interactions, and employing modified couple stress theory to reveal the hardening effects attributed to the rotational behavior of particles within the structure. By incorporating Von Karman geometric nonlinearity, Reddy’s third-order shear deformation theory and Maxwell’s equations, the governing equations for the nonlinear free vibration of MEE nanobeams are derived using Hamilton’s principle. Finally, a two-step perturbation method is employed to solve these equations. Two-step perturbation method disintegrates the solution process into two stages, iteratively approximating and refining the solution, thereby progressively unraveling the intricate details and enhancing the precision of the solution in a systematic manner. Finally, the nonlinear free vibration behavior of MEE nanobeams is explored under the coupled magnetic-electric-elastic fields, with a focus on the effects of various factors that including length scale parameters, nonlocal parameters, Winkler-Pasternak coefficients, span-to-thickness ratios, applied voltages and magnetic potentials.

High-thermal free vibration analysis of functionally graded microplates using a new finite element formulation based on TSDT and MSCT

Recent advancements in additive manufacturing (AM) have revolutionized the design and production of complex engineering microstructures. Despite these advancements, their mathematical modeling and computational analysis remain significant challenges. This research aims to develop an effective computational method for analyzing the free vibration of functionally graded (FG) microplates under high temperatures while resting on a Pasternak foundation (PF). This formulation leverages a new third-order shear deformation theory (new TSDT) for improved accuracy without requiring shear correction factors. Additionally, the modified couple stress theory (MCST) is incorporated to account for size-dependent effects in microplates. The PF is characterized by two parameters including spring stiffness () and shear layer stiffness (). To validate the proposed method, the results obtained are compared with those of the existing literature. Furthermore, numerical examples explore the influence of various factors on the high-temperature free vibration of FG microplates. These factors include the length scale parameter (), geometric dimensions, material properties, and the presence of the elastic foundation. The findings significantly enhance our comprehension of the free vibration of FG microplates in high thermal environments. In addition, the findings significantly enhance our comprehension of the free vibration of FG microplates in high thermal environments. In addition, the results of this research will have great potential in military and defense applications such as components of submarines, fighter aircraft, and missiles.

Vibrations in piezothermoelastic micro-/nanobeam with voids utilizing modified couple stress theory

The present study examines the vibrations in micro- and nano-piezothermoelastic beams with voids. In this work, the modified couple stress theory is employed to generate closed-form formulas for deflection, volume fraction, electric potential and temperature distribution. The effects of voids, modified couple stress, beam dimensions and electric potential on energy dissipation (thermoelastic damping) are examined for beams under various boundary conditions. We have established analytical formulas for frequency shift, attenuation and thermoelastic damping. MATLAB software is used to get numerical results and exhibit them visually.

Buckling analysis of medical guidewires based on the modified couple stress theory

Buckling analysis of medical guidewires based on the modified couple stress theory

Bending responses of graphene nanoplatelets reinforced sandwich cylindrical micro panel with piezoelectric layers

Bending responses of a nanocomposite-reinforced cylindrical panel are studied in this article. A cylindrical shell panel is assumed in micro scale and sandwiched by piezoelectric layers. In this article, a micro-size dependent theory named as the modified couple stress theory (MCST) is analytically employed and the kinematic relations are extended through employing shear deformable model in order to investigate the electroelastic bending responses of a three-layered micro-shell bonded between smart layers subjected to an applied voltage, external and internal pressures. The micro-shell is assumed rested on a two parametrically elastic foundation. In order to develop constitutive relations, the mixture’s rule as well as Halpin-Tsai model are utilized to compute governing equations. Electroelastostatic responses are analytically obtained through trigonometric functions. A large extended parametric analysis is presented to explore deflection of the micro-shell with a change in applied voltage, thickness of the piezoelectric layer to radius, length to radius ratio, different characteristics of nanoplatelet reinforcement for the both external and internal pressure. The proposed composite electromechanical structure may be used in the smart structures and systems. A controllable system can be suggested through the usage of graphene nanoplatelets because of flexibility and affecting parameters.